We have applied time-series analysis to sequences of coronal
loop images obtained with the Yohkoh Soft X-Ray Telescope
(SXT). Using images obtained in fast-cadence mode
(\Delta t = 4 sec), we have generated X-ray light
curves and power spectra for multiple subregions of a
number of coronal loops. Our analysis indicates that out
of 544 spectra of loops which
range in length L from 40 Mm to 150 Mm, there are 16
cases where the
X-ray brightness is modulated periodically with
\ge99.5% confidence.
The periods \tau range from 9.6 sec to 61.6 sec, and the
amplitudes
range from 0.4% to 1.8%. Our result is statistically
significant at the 8\sigma level.

The observed periods can hardly be due to
fluctuations in gas pressure:
temperatures estimated from image ratios indicate
sound speeds of 200 --
280 km/sec, with loop crossing times of hundreds of
seconds. On the other
hand, the ratio 2 L / \tau yields ``velocities"
of 2 -- 14 Mm/sec: these
overlap with published estimates of Alfvén speeds
v_A in coronal
loops, 3.5 -- 37 Mm/sec (Schmelz et al., 1994,
ApJ, 434, 786). Now, in
the context of coronal
loop heating by resonant absorption of MHD waves,
the period \tau_g
\approx 2 L / v_A plays a key role: loops which
are oscillating in their
global mode (with period \tau_g) are maximally
efficient at absorbing
energy (Steinolfson and Davila, 1993,
ApJ, 415, 354). We suggest
that the loops which we
have found to be modulated periodically are
oscillating in their global
mode. With this interpetation, we find that the
plasma beta in the loops
lies in the range \beta _p = 0.001 -- 0.045.
According to the
oscillating loop model of Zaitsev and Stepanov
(1989, Sov. Astron. Letters, 15, 66),
loops with such \beta _p values should be modulated with
amplitudes of 1.1% or less:
our data are consistent with at least the
upper limit of this prediction.